# M**aths**

**Welcome to the Mathematics Department!**

**“Go down deep enough into anything and you will find mathematics.” - Dean Schlicler**

Mathematics is important in everyday life. It helps us to make sense of the world we live in and to manage our lives.

Mathematics engages learners of all ages, interests and abilities. Learning mathematics develops logical reasoning, analysis, problem-solving skills, creativity, and the ability to think in abstract ways. It uses a universal language of numbers and symbols, which allows us to communicate ideas in a concise, unambiguous and rigorous way.

Using mathematics enables us to model real-life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.

Within the Maths Department we aim to create an environment that is safe, nurturing and enjoyable, where young people can acquire the skills and attributes for lifelong learning.

**Staff List **

**Mr Connor (PTC Business., Computing and Maths) **

**Mrs. Greenslade**

** Mr. McNinch **

**Miss. Dawson **

**Mrs. Curran **

** Mr. Ness **

**Miss. McGrath **

**Mr. Mackie **

**Mr Kitsos**

**Mrs Kent**

**USEFUL WEBSITES**

Below are links to some useful maths websites:

https://www.bbc.co.uk/bitesize/subjects/z6vg9j6

https://www.mathsrevision.com/

https://www.national5maths.co.uk/free-national-5-maths-2/

http://www.sptamaths.co.uk/files2/courses.html

https://www.mathsworkout.co.uk/

(username and password required – ask your teacher for this)

**CAREERS IN MATHS:**

### COURSE OUTLINES:

### BROAD GENERAL EDUCATION (S1-S3)

**Your learning in S1 – S3 maths should enable you to:**

- Develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different contexts, including the world of work
- Engage with more abstract mathematical concepts and develop important new kinds of thinking
- Understand the application of mathematics, its impact on our society past and present, and its potential for the future
- Develop essential numeracy skills which will allow me to participate fully in society
- Establish firm foundations for further specialist learning
- Understand that successful independent living requires financial awareness, effective money management, using schedules and other related skills
- Interpret numerical information appropriately and use it to draw conclusions, assess risk, and make reasoned evaluations and informed decisions
- Apply skills and understanding creatively and logically to solve problems, within a variety of contexts
- Appreciate how the imaginative and effective use of technologies can enhance the development of skills and concepts.

**Topics Covered**

**S1 MATHS**

- Whole Numbers and Decimals
- Negative Numbers and Co-ordinates
- Fractions
- Statistics
- Time
- Algebra
- Percentages
- Length and Perimeter
- Area and Volume
- Angles
- Symmetry
- Straight Line

**S2 MATHS**

- Special Numbers
- Algebra
- Whole Numbers and Decimals
- Fractions
- 2D and 3D Shapes
- Pythagoras
- Angles and Circles
- Percentages
- Patterns and Sequences
- Impact of Mathematics
- Probability
- Ration and Proportion
- Scale Drawings and Bearings
- Financial Education
- Trigonometry

**S3 MATHS**

**Level 3**

**Numeracy**

Whole Numbers, Time, Reading Tables, Decimals, Positive and Negative Numbers, Length and Scale, Money, Interpreting Graphs, Fractions and Percentages, Probability, Weight and Capacity

__Shape, Space and Measure__

Perimeter and Area, Directions, Timetables, Volume, Tiling and Symmetry, Scale Drawing, Units of Measurement, Number Patterns

__ Manage Money and Data__Income and Expenditure, Wages and Salaries, VAT, Budgets, Savings, Best Deal, Graphs, Charts and Tables

**Level 4**

**Numeracy**

Calculations and Standard Form, Integers, Units of Measurement, Perimeter, Fractions and Percentages, Scale, Ratio and Direct Proportion, Money, Distance, Speed and Time

__Expressions and Formulae____ __

Algebra, Information Handling, Area, Circles, Surface Area of Prisms, Patterns and Sequences, Volume of Prisms, Probability, Rotational Symmetry

__Relationships__

Pythagoras, Angles, Angles in a Circle, Similarity, Trigonometry, Straight Line, Equations and Inequalities, Scattergraphs, Changing the Subject of a Formula

**Level 4+**

__Applications__

Working with Percentages, Working with Fractions, Trigonometry

__Expressions and Formulae__** **

Expansion of Brackets, Factorising, Volume (and Significant Figures), Straight Line, Arcs and Sectors, Working with Surds, Equations and Inequations, Changing the Subject of a Formula, Algebraic Fractions, Functions, Indices, Vectors

__Relationships__

Applying Pythagoras, Properties of 2D Shapes, Statistics, Similarity, Completing the Square, Quadratic Equations, Simultaneous Equations, Further Trigonometry

### NATIONAL 4 MATHS:

**NATIONAL 4 MATHS**

**The Course aims to:**

- Motivate and challenge learners by enabling them to select and apply straightforward mathematical skills in a variety of mathematical and real-life situations
- Develop confidence in the subject and a positive attitude towards further study in mathematics
- Enable the use of numerical data and abstract terms and develop the idea of generalisation
- Allow learners to interpret, communicate and manage information in mathematical form; skills which are vital to scientific and technological research and development
- Develop the learner’s skills in using mathematical language and to explore straightforward mathematical ideas
- Develop skills relevant to learning, life and work in an engaging and enjoyable way

**On successful completion of this Course, the learner could progress to:**

- National 5 Mathematics
- National 5 Applications of Mathematics
- Numeracy (National 5) Unit

**Course Outline:**

**Mathematics: Expressions and Formulae**

The general aim of this Unit is to develop skills linked to straightforward mathematical expressions and formulae. These include the manipulation of abstract terms, the simplification of expressions and the evaluation of formulae. The Outcomes cover aspects of algebra, geometry, statistics and reasoning.

**Mathematics: Relationships**

The general aim of this Unit is to develop skills linked to straightforward mathematical relationships. These include solving equations, understanding graphs and working with trigonometric ratios. The Outcomes cover aspects of algebra, geometry, trigonometry, statistics and reasoning.

**Numeracy**

The general aim of this Unit is to develop learners’ numerical and information handling skills to solve straightforward, real-life problems involving number, money, time and measurement. As learners tackle real-life problems, they will decide what numeracy skills to use and how to apply these skills to an appropriate level of accuracy. Learners will also interpret graphical data and use their knowledge and understanding of probability to identify solutions to straightforward real-life problems involving money, time and measurement. Learners will use their solutions to make and explain decisions.

**Mathematics Test**

This is the Added Value Unit of the National 4 Mathematics Course. The general aim of this Unit is to enable the learner to provide evidence of added value for the National 4 Mathematics Course through the successful completion of a test which will allow the learner to demonstrate breadth and challenge.

**Unit assessment**

All Units are internally assessed. They can be assessed on an individual Unit basis or by using other approaches which combine the assessment for more than one Unit.

They will be assessed on a pass/fail basis within school.

**Conditions of award**

To achieve the National 4 Mathematics Course, learners must pass all of the required Units, including the Added Value Unit. The required Units are shown in the Course outline section. National 4 Courses are not graded and are awarded on a pass/fail basis.

### NATIONAL 4 APPLIED MATHS:

**National 4 Applications of Maths - Course Outline (SQA Referenced)**

**The Course aims to:**

- Motivate and challenge learners by enabling them to select and apply mathematical skills to tackle straightforward real-life problems or situations
- Develop the ability to interpret straightforward real-life problems or situations involving mathematics
- Develop confidence in the subject and a positive attitude towards the use of mathematics in straightforward real-life situations
- Apply mathematical operational skills with an appropriate degree of accuracy
- Use mathematical reasoning skills to assess risk, draw conclusions and explain decisions
- Communicate mathematical information in an appropriate way

**Course Outline**

**The Course has four Units.**

**Applications of Mathematics: Managing Finance and Statistics**

The general aim of this Unit is to develop skills that focus on the use of mathematical ideas and strategies that can be applied to managing finance and statistics in straightforward real-life contexts. This includes using skills in budgeting as well as skills in organising and presenting data, to explain solutions and/or draw conclusions. The Outcomes cover aspects of finance and statistics in real-life situations requiring mathematical reasoning.

**Applications of Mathematics: Geometry and Measures**

The general aim of this Unit is to develop skills that focus on the use of mathematical ideas and strategies that can be applied to geometry and measurement in straightforward real-life contexts. This includes using skills in interpreting and in using shape, space and measures to determine and explain solutions. The Outcomes cover aspects of geometry and measurement in real-life situations requiring mathematical reasoning.

**Numeracy**

The general aim of this Unit is to develop learners’ numerical and information handling skills to solve straightforward, real-life problems involving number, money, time and measurement. As learners tackle real-life problems, they will decide what numeracy skills to use and how to apply these skills to an appropriate level of accuracy. Learners will also interpret graphical data and use their knowledge and understanding of probability to identify solutions to straightforward real-life problems involving money, time and measurement. Learners will use their solutions to make and explain decisions.

**Added Value Unit: Applications of Mathematics Test**

The general aim of this Unit is to enable the learner to provide evidence of added value for the National 4 Applications of Mathematics Course through successful completion of a test which will allow the learner to demonstrate breadth and application. Breadth and application will be demonstrated through the use of mathematical ideas and strategies that can be applied to organising and planning straightforward aspects in personal life, the workplace and the wider world. This will include the application and integration of financial, measurement, geometric and statistical skills in real-life contexts involving reasoning. Numerical skills underpin all aspects of the Unit and the ability to use these without the aid of a calculator will also be assessed.

To achieve the National 4 Applications of Mathematics Course, learners must pass all of the required Units, including the Added Value Unit. The required Units are shown in the Course outline section. National 4 Courses are not graded and awards are made on a pass/fail basis.

All Units are internally assessed. They can be assessed on an individual Unit basis or by using other approaches which combine the assessment for more than one Unit.

They will be assessed on a pass/fail basis within school.

### NATIONAL 5:

**National 5 - Course Outline (SQA Referenced)**

**The course aims to:**

- Motivate and challenge learners by enabling them to select and apply mathematical techniques in a variety of mathematical and real-life situations
- Develop confidence in the subject and a positive attitude towards further study in mathematics
- Develop skills in manipulation of abstract terms to generalise and to solve problems
- Allow learners to interpret, communicate and manage information in mathematical form: skills which are vital to scientific and technological research and development
- Develop learners’ skills in using mathematical language and in exploring mathematical ideas
- Develop skills relevant to learning, life and work in an engaging and enjoyable way

**Skills, knowledge and understanding for the course**

**The following provides a broad overview of the subject skills, knowledge and understanding developed in the course:**

- Understand and use mathematical concepts and relationships
- Select and apply numerical skills
- Select and apply skills in algebra, geometry, trigonometry and statistics
- Use mathematical models
- Use mathematical reasoning skills to interpret information, to select a strategy to solve a problem, and to communicate solutions

**Topics**

**The National 5 course covers the following topics:**

- Brackets
- Factorisation
- Volume
- Surds and Indices
- Gradient of a Straight Line
- Algebraic Fractions
- Arcs and Sectors
- Straight Line
- Equations and Inequations
- Similar Shapes
- Quadratic Functions and Quadratic Equations
- Pythagoras’ Theorem
- Simultaneous Equations
- Properties of Shapes
- Changing the Subject of a Formula
- Trigonometric Functions
- Percentages
- Trigonometry
- Fractions
- Vectors
- Statistics
- Scatter Graphs

**Course Assessment Structure**

The grade awarded is based on the total marks achieved across all course assessment components. Achievement of this course gives automatic certification of the following Core Skill:

**Numeracy at SCQF level 5**

**Component 1: question paper 1 (non-calculator) 50 marks**

This question paper is set and marked by SQA, and conducted in school under conditions specified for external examinations by SQA.

Learners complete this in 1 hour and 15 minutes.

**Component 2: question paper 2 (calculator) 60 marks**

This question paper is set and marked by SQA, and conducted in school under conditions specified for external examinations by SQA.

Learners complete this in 1 hour and 50 minutes.

### National 5 Applications of Maths - Course Outline (SQA Referenced)

**The course aims to:**

- Motivate and challenge learners by enabling them to select and apply mathematical techniques in a variety of real-life situations
- Develop the ability to analyse real-life problems or situations with some complex features involving mathematics
- Develop confidence in the subject and a positive attitude towards the use of mathematics in real-life situations
- Develop the ability to select, apply, combine and adapt mathematical operational skills to new and unfamiliar situations in life and work to an appropriate degree of accuracy
- Develop the ability to use mathematical reasoning skills to generalise, build arguments, draw logical conclusions, assess risk, and make informed decisions
- Develop the ability to use a range of mathematical skills to analyse, interpret and present a range of information
- Develop the ability to communicate mathematical information in a variety of forms
- Develop the ability to think creatively and in abstract ways

**Skills, knowledge and understanding for the course**

**The following provides a broad overview of the subject skills, knowledge and understanding developed in the course:**

- Analyse real-life situations and problems involving mathematics
- Identify valid mathematical operational skills to tackle real-life situations or problems
- Select and apply numeracy skills
- Select and apply skills in finance, statistics, measurement, geometry, graphical data and probability
- Use mathematical reasoning skills to draw conclusions or justify decisions
- Communicate mathematical information in an appropriate way

**Course assessment structure**

**Component 1: question paper 1 (non-calculator) 45 marks**

This question paper is set and marked by SQA, and conducted in school under conditions specified for external examinations by SQA.

Learners complete this in 1 hour and 5 minutes.

**Component 2: question paper 2 65 marks**

Learners complete this in 2 hours (including time to read and absorb case study information).

The grade awarded is based on the total marks achieved across all course assessment components. Achievement of this course gives automatic certification of the following Core Skill:

· Numeracy at SCQF level 5

### HIGHER:

**Higher - Course Outline (SQA Referenced)**

**The course aims to:**

- ·Motivate and challenge learners by enabling them to select and apply mathematical techniques in a variety of mathematical situations
- Develop confidence in the subject and a positive attitude towards further study in mathematics and the use of mathematics in employment
- Deliver in-depth study of mathematical concepts and the ways in which mathematics describes our world
- Allow learners to interpret, communicate and manage information in mathematical form, skills which are vital to scientific and technological research and development
- Deepen learners’ skills in using mathematical language and exploring advanced mathematical ideas

**Skills, knowledge and understanding for the course**

**The following provides a broad overview of the subject skills, knowledge and understanding developed in the course:**

- Understand and use a range of complex mathematical concepts and relationships
- Select and apply operational skills in algebra, geometry, trigonometry, calculus and statistics within mathematical contexts
- Select and apply skills in numeracy
- Use mathematical reasoning skills to extract and interpret information and to use complex mathematical models
- Use mathematical reasoning skills to think logically, provide justification or proof, and solve problems
- Communicate mathematical information with complex features

**Topics**

**The Higher course covers the following topics:**

- Straight Lines
- Recurrence Relations
- Functions and Graphs
- Trigonometric Graphs (and Radians)
- Differentiation
- Integration
- Circles
- Quadratic Theory
- Polynomials
- Trigonometry
- Further Calculus
- Vectors
- Logarithmic and Exponential Functions
- Wave Function

**Course assessment structure**

**The grade awarded is based on the total marks achieved across all course assessment components. Achievement of this course gives automatic certification of the following Core Skill:**

· Numeracy at SCQF level 6

**Component 1: question paper 1 (non-calculator) 70 marks**

Learners have 1 hour and 30 minutes to complete this question paper.

**Component 2: question paper 2 (calculator) 80 marks**

Learners have 1 hour and 45 minutes to complete this question paper

### ADVANCED HIGHER:

**Advanced Higher - Course Outline (SQA Referenced)**

**The course aims to:**

- Motivate and challenge learners by enabling them to select and apply complex mathematical techniques in a variety of mathematical situations
- · Extend learners’ skills in problem solving and logical thinking
- Clarify learners’ thinking through the process of rigorous proof
- Allow learners to interpret, communicate, and manage information in mathematical form, skills which are vital to scientific and technological research and development
- Develop confidence in the subject and a positive attitude towards further study in mathematics and the use of mathematics in employment
- Deliver in-depth study of mathematical concepts and the ways in which mathematics describes our world
- Deepen learners’ skills in using mathematical language and exploring advanced mathematical ideas

**Skills, knowledge and understanding for the course**

- Using mathematical reasoning skills to think logically, provide justification, and solve problems
- Knowledge and understanding of a range of complex concepts
- Selecting and applying complex operational skills
- Using reasoning skills to interpret information and complex mathematical models
- Effectively communicating solutions in a variety of contexts
- Explaining and justifying concepts through the idea of rigorous proof
- Thinking creatively

**Topics**

**The Advanced Higher Course covers the following topics:**

- Partial Fractions
- Arithmetic Sequences
- Product Rule
- MacLauren Series
- Implicit and Parametric Differentiation
- Binomial Theorem
- Complex Numbers
- Integration
- Complex Numbers
- 1st Order Differential Equations
- Matrices
- Integrating Factor
- Gaussian Elimination
- Vectors
- Graphs of Functions
- Optimisation
- Proofs
- Counter Examples
- Euclidean Algorithms

**Course assessment structure: question paper**

The grade awarded is based on the total marks achieved across both course assessment components.

**Question paper 1 (non-calculator) 35 marks**

Learners have 1 hour to complete this question paper.

**Question paper 2 (calculator) 80 marks**

Learners have 2 hours and 30 minutes to complete this question paper.

### HOMEWORK POLICY

**HOMEWORK POLICY**

S1 and S2 pupils will be asked to complete exercises that consolidate the work done in class.

Pupils in S3 – S6 will be set formal exercises at regular intervals, with several days’ notice.

Pupils can expect to receive homework every one to two weeks, with varying completion times.

Your teacher should mark and return your homework with comments on your strengths and areas for improvement.